High-speed combustion devices experience a variety of complex and tightly-coupled physical phenomena that render system design analyses extremely challenging. At the heart of these systems, compressible turbulent air streams, often at supersonic speeds, mix with fuel at time scales on the same order of magnitude as the chemical reactions that drive the combustion process. In practical systems, a number of competing effects, such as heat transfer to the combustor walls and the thermochemistry of the fuel source itself, can significantly alter this process, resulting in operational envelopes with enhanced sensitivity to system design. These complexities are hard to reproduce and study experimentally. As such, numerical simulations are an important tool for understanding these high-speed combustion environments. Using these tools in a design environment, however, remains a challenge. First principles simulations can be prohibitively expensive, and reduced-order models can be difficult to design and calibrate. The level of fidelity needed to model such complex flows varies on a case-to-case basis and may not even be known prior to beginning an investigation. Therefore, there is an ongoing need for understanding the fundamental physics associated with these complex combustion environments. This opportunity is focused on building on the fundamentals of chemically reacting fluid dynamics to develop better numerical simulation methods to achieve a more thorough understanding of the complex physics found within high-speed combustion devices. Potential topics include but are not limited to developing novel numerical methods for simulating multicomponent chemically reacting flows, performing direct numerical simulations of compressible chemically reacting flows in relevant systems, improving our understanding of the multimaterial heat transfer processes between chemically reacting gases and combustor walls, investigating the fundamentals of distributed or flameless combustion processes, simulating the mixing of chemically reacting supercritical fuels with compressible high-speed air, understanding flame sensitivity to flame holder and other geometric features of combustors, simulating shocks and detonations in multicomponent gases, identifying the interactions of turbulence with detailed chemical reactions, assessing reduced combustion models against detailed kinetics in complex chemically reacting flow environments, and using machine learning and other advanced reduced order modeling concepts in coordination with high fidelity modeling to create efficient and accurate combustion device models.